Hicks theorem: Effects of technological improvement in the Ricardian model

Using the Ricardian model, we formally prove Hicks' [Hicks, John (1953), "An Inaugural Lecture," Oxford Economic Papers 5(2), 117-135.] insight into the effects of technological improvement: uniform technological improvement at home benefits all countries (or at least does not hurt); export-biased technological improvement at home benefits the foreign country (or at least does not hurt), but import-biased technological improvement at home can hurt the foreign country as long as the comparative advantage is not reversed. We then study optimal strategies of technological improvement and show that for a small country it is optimal to choose export-biased technological improvement. For a large country, it is optimal to improve technology in both sectors at a rate proportional to the consumers' expenditure share. Therefore, if the expenditure share of the import sector is larger than that of the export sector, a large country will choose a relatively import-biased technological improvement, which will hurt its trading partner.